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Interference
Review & Summary
Huygens' Principle
The three-dimensional transmission of waves, including light, may often be predicted by Huygens' principle, which
states that all points on a wavefront serve as point sources of spherical secondary wavelets. After a time t, the new
position of the wavefront will be that of a surface tangent to these secondary wavelets.
The law of refraction can be derived from Huygens' principle by assuming that the index of refraction of any medium is
, in which v is the speed of light in the medium and c is the speed of light in vacuum.
Wavelength and Index of Refraction
The wavelength λn of light in a medium depends on the index of refraction n of the medium:
(35-6)
in which is the wavelength in vacuum. Because of this dependency, the phase difference between two waves can
change if they pass through different materials with different indexes of refraction.
Young's Experiment
In Young's interference experiment, light passing through a single slit falls on two slits in a screen. The light leaving
these slits flares out (by diffraction), and interference occurs in the region beyond the screen. A fringe pattern, due to the
interference, forms on a viewing screen.
The light intensity at any point on the viewing screen depends in part on the difference in the path lengths from the slits
to that point. If this difference is an integer number of wavelengths, the waves interfere constructively and an intensity
maximum results. If it is an odd number of half-wavelengths, there is destructive interference and an intensity minimum
occurs. The conditions for maximum and minimum intensity are
(35-14)
(35-16)
where is the angle the light path makes with a central axis and d is the slit separation.
Coherence
If two light waves that meet at a point are to interfere perceptibly, the phase difference between them must remain
constant with time; that is, the waves must be coherent. When two coherent waves meet, the resulting intensity may be
found by using phasors.
Intensity in Two­Slit Interference
In Young's interference experiment, two waves, each with intensity I0, yield a resultant wave of intensity I at the
viewing screen, with
(35-22, 35-23)
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Interference
Equations 35-14 and 35-16, which identify the positions of the fringe maxima and minima, are contained within this
relation.
Thin­Film Interference
When light is incident on a thin transparent film, the light waves reflected from the front and back surfaces interfere. For
near-normal incidence, the wavelength conditions for maximum and minimum intensity of the light reflected from a film
in air are
(35-36)
(35-37)
where n2 is the index of refraction of the film, L is its thickness, and
is the wavelength of the light in air.
If the light incident at an interface between media with different indexes of refraction is in the medium with the smaller
index of refraction, the reflection causes a phase change of
, or half a wavelength, in the reflected wave.
Otherwise, there is no phase change due to the reflection. Refraction causes no phase shift.
The Michelson Interferometer
In Michelson's interferometer a light wave is split into two beams that, after traversing paths of different lengths, are
recombined so they interfere and form a fringe pattern. Varying the path length of one of the beams allows distances to
be accurately expressed in terms of wavelengths of light, by counting the number of fringes through which the pattern
shifts because of the change.
Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.
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